Progress In Galois Theory

Author : Helmut Voelklein,Tanush Shaska
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 55,8 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9780387235349

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Progress in Galois Theory by Helmut Voelklein,Tanush Shaska Pdf

The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implica tions for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).

Author : Pierre Dèbes,Michel Emsalem,Matthieu Romagny,A. Muhammed Uludağ
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 49,5 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034804875

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Arithmetic and Geometry Around Galois Theory by Pierre Dèbes,Michel Emsalem,Matthieu Romagny,A. Muhammed Uludağ Pdf

This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.​

Author : Helmut Voelklein,Tanush Shaska
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 49,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9780387235332

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Progress in Galois Theory by Helmut Voelklein,Tanush Shaska Pdf

The theme of this book are the interactions between group theory and algebra/geometry/number theory, showing ubiquity and power of the basic principle of Galois theory. The book presents recent developments in a major line of work about covers of the projective line (and other curves), their fields of definition and parameter spaces, and associated questions about arithmetic fundamental groups. This is intimately tied up with the Inverse Problem of Galois Theory, and uses methods of algebraic geometry, group theory and number theory.

Author : Gunter Malle,B. Heinrich Matzat
Publisher : Springer
Page : 533 pages
File Size : 42,7 Mb
Release : 2018-07-27
Category : Mathematics
ISBN : 9783662554203

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Inverse Galois Theory by Gunter Malle,B. Heinrich Matzat Pdf

A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 47,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475768985

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Undergraduate Algebra by Serge Lang Pdf

The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 52,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642591419

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Galois Cohomology by Jean-Pierre Serre Pdf

This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.

Author : Steven H. Weintraub
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 44,9 Mb
Release : 2008-10-20
Category : Mathematics
ISBN : 9780387875750

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Galois Theory by Steven H. Weintraub Pdf

Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.

Author : Ki-ichiro Hashimoto,Katsuya Miyake,Hiroaki Nakamura
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 49,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302490

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Galois Theory and Modular Forms by Ki-ichiro Hashimoto,Katsuya Miyake,Hiroaki Nakamura Pdf

This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.

Author : Juan J. Morales Ruiz
Publisher : Birkhäuser
Page : 177 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887182

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Differential Galois Theory and Non-Integrability of Hamiltonian Systems by Juan J. Morales Ruiz Pdf

This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system. The underlying heuristic idea, which motivated the main results presented in this monograph, is that a necessary condition for the integrability of a Hamiltonian system is the integrability of the variational equation along any of its particular integral curves. This idea led to the algebraic non-integrability criteria for Hamiltonian systems. These criteria can be considered as generalizations of classical non-integrability results by Poincaré and Lyapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several important applications are also included: homogeneous potentials, Bianchi IX cosmological model, three-body problem, Hénon-Heiles system, etc. The book is based on the original joint research of the author with J.M. Peris, J.P. Ramis and C. Simó, but an effort was made to present these achievements in their logical order rather than their historical one. The necessary background on differential Galois theory and Hamiltonian systems is included, and several new problems and conjectures which open new lines of research are proposed. - - - The book is an excellent introduction to non-integrability methods in Hamiltonian mechanics and brings the reader to the forefront of research in the area. The inclusion of a large number of worked-out examples, many of wide applied interest, is commendable. There are many historical references, and an extensive bibliography. (Mathematical Reviews) For readers already prepared in the two prerequisite subjects [differential Galois theory and Hamiltonian dynamical systems], the author has provided a logically accessible account of a remarkable interaction between differential algebra and dynamics. (Zentralblatt MATH)

Author : Ian Stewart
Publisher : Unknown
Page : 0 pages
File Size : 46,5 Mb
Release : 2021
Category : Galois theory
ISBN : 7560396437

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Galois Theory (Fourth Edition) by Ian Stewart Pdf

Author : Steffen Gielen,Sylvain Carrozza,Daniele Oriti
Publisher : MDPI
Page : 338 pages
File Size : 55,6 Mb
Release : 2020-07-01
Category : Mathematics
ISBN : 9783039361786

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Progress in Group Field Theory and Related Quantum Gravity Formalisms by Steffen Gielen,Sylvain Carrozza,Daniele Oriti Pdf

Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.

Author : Jean-Pierre Escofier
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301912

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Galois Theory by Jean-Pierre Escofier Pdf

This book offers the fundamentals of Galois Theory, including a set of copious, well-chosen exercises that form an important part of the presentation. The pace is gentle and incorporates interesting historical material, including aspects on the life of Galois. Computed examples, recent developments, and extensions of results into other related areas round out the presentation.

Author : Gunter Malle,B.H. Matzat
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 54,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662121238

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Inverse Galois Theory by Gunter Malle,B.H. Matzat Pdf

A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.

Author : Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason
Publisher : Springer
Page : 453 pages
File Size : 43,6 Mb
Release : 2015-09-04
Category : Science
ISBN : 9783319213538

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Advances in Algebraic Quantum Field Theory by Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason Pdf

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Author : J. Ambjorn,B.J. Durhuus,J.L. Petersen
Publisher : Elsevier
Page : 307 pages
File Size : 50,6 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780444598394

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Recent Developments in Quantum Field Theory by J. Ambjorn,B.J. Durhuus,J.L. Petersen Pdf

Theoretical particle physicists discuss the present status and, in particular, the latest developments in quantum field theory, in their broadest aspects. This volume contains the main lectures presented at the symposium and reflects the contemporary status of a line of development, one of whose initiators was Niels Bohr.